Balancing, filtering and/or controlling series-connected cells

ABSTRACT

A balancing circuit for a plurality of series connected cells or substrings of cells is provided. In one implementation, the balancing circuit includes a plurality of primary ports; an isolated secondary port; and one or more DC-DC converters connected between the primary ports and the isolated secondary port. Each DC-DC converter includes at least one power switch. The DC-DC converters are configured to adjust a primary port current received at one or more of the plurality of primary ports based upon a difference between a voltage at the one of the primary ports and a reference voltage. Also provided are an electrical power system including such as balancing circuit and a method of balancing a plurality of electric cell substrings using such a balancing circuit.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of (1) U.S. provisional applicationNo. 61/657,870 entitled “Balancing, Filtering, and/or Controlling SeriesConnected Cells” and filed on Jun. 10, 2012 (the '870 application), and(2) U.S. provisional application No. 61/785,196 entitled “Balancing,Filtering and/or Controlling Series-Connected Cells” and filed on Mar.14, 2013 (the '196 application). Both the '870 and '196 application arehereby incorporated by reference in their entirety as though fully setforth herein.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under grant numberDE-AR0000216 awarded by the U.S. Department of Energy. The governmenthas certain rights in the invention.

BACKGROUND

a. Field

The instant invention relates to systems, methods and components forbalancing, filtering and/or controlling series connected electricalcells.

b. Background

Electrical power systems such as photovoltaic (PV) power systems orenergy-storage (battery) systems (BS) commonly comprise a large numberof cells connected in series. The series connection implies that thesystem performance, such as energy capture in PV systems or energystorage capacity in battery systems, is constrained by the performanceof the weakest cell. As a result, the electrical power systems based onseries-connected cells are adversely affected by any mismatches amongthe cells. Example balancing circuits and control methods are providedbased on isolated DC-DC converters processing only a mismatch fractionof power.

BRIEF SUMMARY

Various example balancing approaches described herein, which are simpleand scalable, can result in significant system performance improvementsin the presence of mismatches, while introducing no or at least minimalinsertion loss penalties.

A balancing circuit for a plurality of series connected cells orsubstrings of cells is provided. In one implementation, the balancingcircuit includes a plurality of primary ports; an isolated secondaryport; and one or more DC-DC converters connected between the primaryports and the isolated secondary port. Each DC-DC converter includes atleast one power switch. The DC-DC converters are configured to adjust aprimary port current received at one or more of the plurality of primaryports based upon a difference between a voltage at the one of theprimary ports and a reference voltage. Also provided are an electricalpower system including such as balancing circuit and a method ofbalancing a plurality of electric cell substrings using such a balancingcircuit.

In addition, examples of a simple and scalable cell balancing approachwith built-in filtering are also provided. In various embodiments, thecombined balancing and filtering circuits and control techniques resultin significant system performance improvements in the presence ofmismatches among the cells or substrings of cells. At the same time, thefiltering is accomplished at reduced cost and with improved reliability.

A control technique for balancing circuits is also provided. The controltechnique, which applies to substring DC-DC converters, simplifiesgeneration of reference signals, and simultaneously achieves balancingand voltage regulation across the secondary port of the substring DC-DCconverters.

The foregoing and other aspects, features, details, utilities, andadvantages of the present invention will be apparent from reading thefollowing description and claims, and from reviewing the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1, including FIGS. 1A and 1B, show an example photovoltaic moduleand an electrical circuit diagram of the photovoltaic module.

FIG. 2A shows a series connected photovoltaic modules or panels with astring or central inverter.

FIG. 2B shows photovoltaic modules with module-integrated DC-DCconverters, also known as DC optimizers.

FIG. 2C shows photovoltaic modules with micro-inverters.

FIG. 3 shows a conventional battery system for hybrid electric vehicles(HEV), plug-in hybrid electric vehicles (PHEV), or electric vehicles(EV).

FIG. 4, including FIGS. 4A and 4B, show another example photovoltaicmodule and an electrical circuit diagram including an exampleimplementation of a balancing circuit for the photovoltaic module.

FIG. 5 shows power versus voltage characteristics of the conventional PVmodule of FIG. 1, and of the PV module with the balancing circuit shownin FIG. 4.

FIGS. 6A, 6B and 6C show various implementations of substring DC-DCconverters with isolation based on (a) an isolation transformer, (b) atransmission-line or coaxial isolation transformer, or (c) isolationcapacitors 90, respectively.

FIG. 7 shows an example implementation of an electric power system withseries-connected cells or cell substrings and a balancing circuit.

FIG. 8 shows another example implementation of an electric power systemwith series connected cells or cell substrings and a balancing circuit,with a secondary circuit connected to the secondary port.

FIG. 9 shows yet another example implementation of an electric powersystem with series connected cells or cell substrings and a balancingcircuit.

FIGS. 10A through 10E show several embodiments of example cellsubstrings that may be used with the balancing circuits describedherein.

FIG. 11 shows another example implementation of an electric power systemwith series connected battery cells or battery cell substrings and abalancing circuit.

FIG. 12 shows an example block diagram of a controller for a substringDC-DC converter in a balancing circuit.

FIGS. 13A through 13C show multiple examples of controller compensatorsteady-state (DC) characteristics.

FIG. 14 shows another example implementation of a controller for asubstring DC-DC converter in one or more of the balancing circuitsdescribed herein.

FIGS. 15A and 15B show an example implementation of a photovoltaicmodule and an electrical circuit diagram including an exampleimplementation of a balancing circuit for the photovoltaic module with abalancing and filtering circuit.

FIG. 16A shows an example implementation of an electrical power systemin which an example implementation of a balancing/filtering circuit forthe electrical power system is coupled to an AC output via a DC-ACinverter.

FIG. 16B shows example AC output waveforms of the balancing/filteringcircuit shown in FIG. 16A.

FIG. 17A shows an example implementation of an electrical systemcomprising a plurality of series connected cells with a balancingcircuit where a secondary port of the balancing circuit is isolated.

FIG. 17B shows an example implementation of an electrical systemcomprising a plurality of series connected cells with a balancingcircuit where a secondary port of the balancing circuit is connectedacross the output of the string of series-connected cell substrings.

FIG. 18 shows an example implementation of a block diagram of asubstring DC-DC converter controller.

FIG. 19 shows an example implementation diagram in which a centralcontroller and only one module-level current sensor are provided.

FIG. 20 shows an example substring and a corresponding subMIC thatregulates the substring voltage to a reference proportional to asecondary port voltage v_(mod).

FIG. 21 shows an example distributed subMIC control approach that doesnot require a central controller.

FIG. 22 shows an example implementation of a photovoltaic arraycomprising a plurality of series-connected subMIC-enhanced moduleshaving shared secondary ports and built-in balancing.

FIG. 23 shows an example implementation in which each subMIC isimplemented as a bidirectional flyback converter.

FIG. 24A shows an example implementation of a photovoltaic systemincluding a SubMIC-enhanced module and a microinverter.

FIG. 24B shows an example implementation of a photovoltaic systemincluding a SubMIC-enhanced module and a DC optimizer.

FIG. 25 shows an example implementation of a photovoltaic systemincluding a string of SubMIC-enhanced modules and one or more stringinverters or a central inverter.

FIG. 26 shows another example implementation of a photovoltaic systemincluding a string of SubMIC-enhanced modules and one or more stringinverters or a central inverter in which an isolated secondary port isshared among the modules.

DETAILED DESCRIPTION

FIGS. 1A and 1B show an example photovoltaic (PV) module 10 and anelectrical circuit diagram 20 of the photovoltaic module 10. Inparticular, FIG. 1A shows the photovoltaic module 10 including threephotovoltaic cell substrings 12, 14, 16 connected in series with twentyfour individual photovoltaic cells 18 per string 12, 14, 16. FIG. 1Bshows the electrical circuit diagram 20.

In the example shown in FIGS. 1A and 1B, seventy two photovoltaic cells18 are connected in series. The cells 18 are grouped in threeseries-connected substrings 12, 14, 16, with twenty four cells 18connected in series in each substring 12, 14, 16. A parallel (also knownas backplane or bypass) diode 22 is connected in parallel with eachsubstring 12, 14, 16. A purpose of the backplane diode 22 is to preventreverse bias and excessive power dissipation on the photovoltaic cells16 (known as “hot spot”) when the photovoltaic module 10 is partiallyshaded. Partial shading occurs when the solar irradiation (also known as“insolation”) on some of the photovoltaic cells 18 is higher than thesolar irradiation on other cells 18. Mismatches among photovoltaic cellsare due to partial shading and other causes, such as manufacturingtolerances, temperature gradients, or dirt. The backplane diode 22bypasses a weaker substring of photovoltaic cells 18 allowing thecurrent of stronger substrings to flow through to the output. A reversebias of the cells 18 in the weaker substring is prevented, thus avertinghot-spot failures. However, conduction of bypass diodes 22 reduces theoutput voltage of the module 10 and thereby reduces the output power ofthe module 10 as well.

A conventional photovoltaic system 30 typically includes a number ofphotovoltaic modules 32 (such as the module 10 example shown in FIGS. 1Aand 1B) connected in series, such as shown in FIG. 2A. The seriesconnected modules 32 are coupled, such as via a string inverter 34, toan AC electric grid 36. The series connection of the plurality ofphotovoltaic modules 32 further exacerbates the mismatch-induced loss inpower output and energy capture of each module, diminishing theefficiency of the photovoltaic system 30. It has been found thatmismatches due to partial shading or other reasons result in significantlosses in energy capture, especially in residential or commercialrooftop photovoltaic systems.

Many approaches have been proposed to address the mismatch-induced lossin efficiency and energy capture in photovoltaic systems, includingmodule-integrated DC-DC converters 38 as shown in FIG. 2B, ormicro-inverters 40 as shown in FIG. 2C. In these architectures, powerelectronics converters (DC-DC converters 38 or inverters 40) aredistributed across the photovoltaic system and typically tied to eachindividual photovoltaic module 32. The converters 38 are controlled toperform per-module 32 maximum power point tracking, thus alleviating theloss in efficiency and energy capture due to mismatches amongphotovoltaic modules 32. However, the approaches based onmodule-integrated power electronics converters have several fundamentalproblems such as the following:

(1) the maximum power point tracking at the module level is not able torecover energy loss due to cell or substring mismatches within a module;

(2) power converters must process full photovoltaic module power at alltimes, which results in additional insertion losses even when all cells,substrings, and modules are well matched;

(3) power converters must be rated at full photovoltaic module power,which increases the converter and system cost.

The fact that substring or cell level power conversion could havesignificant potential benefits in improved photovoltaic systemefficiency and improved energy capture has been discussed, but theproblem of increased implementation cost and complexity has not beenaddressed. An approach based on partial power processing has beendescribed, but it requires more complex installation and wiring, andmore complex centralized system control.

In one implementation, for example, a simple, scalable andcost-effective balancing of photovoltaic cells or photovoltaicsubstrings within photovoltaic modules in photovoltaic power systems isprovided herein.

The problem of mismatch-related performance loss is also present inother electric power systems based on series-connected cells. Forexample, energy-storage systems typically include many electrochemical(battery) cells connected in series. For example, FIG. 3 shows aconventional battery system for hybrid electric vehicles (HEV), plug-inhybrid electric vehicles (PHEV), or electric vehicles (EV). Regardlessof the chemistry specifics, a single battery cell voltage V_(cell) isrelatively low (e.g., several volts). On the other hand, efficientoperation of the electric drive propulsion (including power electronicsinverters/rectifiers and electric machines) requires a relatively highDC voltage bus voltage V_(DC) (e.g., several hundred volts). The voltagemismatch between a battery cell and the DC bus voltage is commonlyresolved by placing a large number (n) of battery cells in series, asshown in FIG. 3. With n in the order of 100, the resulting battery packvoltage V_(bat)=nV_(cell) is typically much closer to the required DCbus voltage V_(DC). A fundamental problem in this system is related tothe series connection of the battery cells: the system is only as goodas the weakest cell in the string. Furthermore, if unattended,mismatches among the cells (e.g., due to manufacturing tolerances,temperature gradients across the pack, and mismatched degradation overcycle and calendar life) can lead to overcharging or excessive dischargeof individual cells, resulting in rapid cell failures and severe cyclelife limits. In the case of Lithium-Ion cell chemistries, which areconsidered most likely candidates for PHEV and EV applications, eachcell in the string must include protection devices to preventcatastrophic failures due to overcharge, excessive discharge, or excesstemperature.

A sophisticated battery management system (BMS) 50 is typically usedaround the string of cells 52, as shown in FIG. 3. The BMS 50 monitorscurrent, temperature, as well as cell voltages to assess the batterystate of charge (SOC) and the state of health (SOH), which are thencommunicated to a vehicle system controller 54. The BMS 50 functionsinclude cell protection, charge control, operation of the battery packwithin a target SOC window, and cell balancing, i.e. a way ofcompensating for weaker cells by equalizing the charge on all the cells52 in the string and thus extending the battery system life. Inpractice, even with the BMS 50, the string length (i.e. the number n ofcells 52 in series) is limited. An additional bidirectional DC bus DC-DCconverter 56 is therefore often installed between the battery pack andthe electric drive propulsion components 58, regulating the propulsionDC bus voltage V_(DC). Cell balancing can be passive or active. In thepassive case, balancing results in power losses and is relatively slow.Although many active balancing schemes have been proposed, a new simple,scalable and cost-effective cell balancing and power management isprovided herein for battery systems.

Other electric power systems that benefit from simple, scalable andcost-effective balancing of series-connected cells or substrings includesystems based on capacitors or super-capacitors, solid-state lighting(LED) systems, thermoelectric couples or other systems with electricalor electronic components or modules connected in series.

Balancing Series-Connected Cells

FIGS. 4A and 4B show an example implementation of a balancing circuit 60for a plurality of series-connected cells, such as the shownseries-connected photovoltaic cells 62. In this particularimplementation, the balancing circuit 60 includes is shown in a typicalphotovoltaic module 61 having seventy two photovoltaic cells 62 arrangedin three substrings 64, 66, 68, each substring 64, 66, 68 having twentyfour photovoltaic cells 62 connected in series. The balancing circuit 60comprises a plurality of substring DC-DC converters 70. A substringDC-DC converter, also called sub-module integrated converter or SubMIC70 has a primary port (voltage V_(p)) 72 and an isolated secondary port(voltage V_(s)) 74. The secondary port and the primary port of the DC-DCconverter are isolated. The primary port 72 of a substring DC-DCconverter 70 is connected in parallel with a substring 64, 66, 68 ofcells 62 in the photovoltaic module 61. The secondary ports 74 of allsubstring DC-DC converters 70 are connected in parallel. Each substringDC-DC converter comprises at least one controllable power switch.Additionally, each substring DC-DC converter 70 uses a reference voltageas described herein. The reference voltage, for example, may beproportional to the secondary isolated port voltage or proportional tothe module output voltage V_(o) (e.g., FIGS. 17A and 17B). The balancingcircuit 60 operates by diverting primary-port current (I_(p)>0) from, orby injecting primary-port current (I_(p)<0) to the corresponding cellsubstring 64, 66, 68. Consider, for example, the case when two substringcurrents are matched, I₁=I₂=I, while the third substring current ismismatched, I₃=0, so that the total output power available from thesubstrings 64, 66, 68 is reduced by one third. In response, thesubstring DC-DC converter currents are adjusted by controlling the powerswitch so that I_(p1)=I_(p2)=I/3, while I_(p3)=−2I/3. As a result, thephotovoltaic module output current isI_(o)=I₁−I_(p1)=I₂−I_(p2)=I₃−I_(p3)=2I/3, which shows how, using thebalancing circuit 60, the module output power equals the total availablepower from the substrings 64, 66, 68, without a loss of the availablepower. In the case when all substrings 64, 66, 68 are matched, i.e. whenall substring currents are the same, I₁=I₂=I₃=I the substring DC-DCconverters 70 are shut down so that I_(p1)=I_(p2)=I_(p3)=0, and themodule output current simply equals the substring current, I_(o)=I. Inthe well matched case, the balancing circuit adds no insertion or otherlosses.

As another example, consider the case when the first substring 64 isfully irradiated, while the second and third substrings 66 and 68 areshaded to α₂=50% and α₃=70%, respectively. In this example, FIG. 5 showspower versus voltage characteristics of the conventional PV module ofFIG. 1 (shown as MPP (conventional)), and of the PV module with thebalancing circuit 60 shown in FIG. 4 (shown as MPP (full insolation) andMPP (SubMIC)). At a maximum power point, the module with the balancingcircuit produces 40% more power than the conventional PV module.Furthermore, the maximum power point (MPP) in the module with thebalancing circuit occurs at the voltage which is nearly the same as theMPP voltage when the module is fully irradiated. This nearly-constantvoltage output of the PV module with the balancing circuit is verybeneficial to reduce cost and improve efficiency of follow-up powerelectronics in PV systems.

In this implementation, it can be noted that the substring DC-DCconverters (or SubMICs) in the balancing circuit process only themismatch portion of power, which means that the substring converters 70can be significantly smaller in size and cost compared to other moduleintegrated converters or microinverters. Furthermore, in someimplementations, the converters 70 introduce no insertion or otherlosses when the cells or substrings are well matched, thus maximizing orat least increasing the PV system efficiency and energy capture underall operating conditions.

The substring DC-DC converters 70 shown in FIG. 4 have isolation betweenthe primary port and the secondary port. FIGS. 6A, 6B and 6C showvarious implementations of substring DC-DC converters 80, 84, 88 withisolation based on (a) an isolation transformer 82, (b) atransmission-line or coaxial isolation transformer 86, or (c) isolationcapacitors 90. Many well known converter configurations are available torealize isolated substring DC-DC converters (or SubMICs). The substringDC-DC converter with transformer isolation (shown in FIG. 6A), forexample, can be Flyback, Forward, Cuk, Sepic, push-pull, half-bridge,full-bridge, or any other of many available converter configurations.

The substring DC-DC converter with isolation (shown in FIG. 6) can be,for example, a resonant converter such as series-resonant converter,parallel-resonant converter, LLC resonant converter, or radio-frequencyresonant converter. When the substring DC-DC converter is a resonantconverter where the primary port current depends on a difference betweenthe primary port and secondary port voltages, a simple open-loop switchcontrol is sufficient for balancing.

FIG. 7 shows an example implementation of an electric power system 100with series-connected cells or cell substrings 102 and a balancingcircuit 104. The balancing circuit 104 comprises a plurality ofsubstring DC-DC converters 106. Each substring DC-DC converter 106 has aprimary port 108 and a secondary port 110, which are isolated. Theprimary port 108 is connected in parallel with a cell substring 102 soit can add or subtract the current in order to balance the cellsubstrings 102. The secondary ports 110 of the substring DC-DCconverters 106 are connected in parallel. In the implementation shown inFIG. 7, only the secondary ports 110 of the substring DC-DC converters106 and no other circuits are connected in parallel to form secondaryvoltage V_(s). Thus, the secondary ports 106 are isolated. Eachsubstring DC-DC converter 106 further determines or receives a referencevoltage proportional to the secondary isolated port voltage.

FIG. 8 shows another example implementation of an electric power system120 similar to the electric power system 100 shown in FIG. 7. In theimplementation shown in FIG. 8, the electric power system 120 comprisesa plurality of cell substrings 122 coupled to a balancing circuit 124.In this implementation, the balancing circuit 124 comprises a pluralityof substring DC-DC converters 126. Each substring DC-DC converter 126has a primary port 128 and a secondary port 130. The primary port 128 isconnected in parallel with a cell substring 122 so it can add orsubtract the current in order to balance the cell substrings 122. Thesecondary ports 130 of the substring DC-DC converters 106 are connectedin parallel and are further coupled to an additional secondary circuit132. The secondary circuit 132 can be, for example, a voltage source orsink, a current source or sink, a power source or sink, a load, oranother power converter. Each substring DC-DC converter 126 furtherdetermines or receives a reference voltage proportional to the secondaryisolated port voltage, or a reference voltage proportional to theelectric power system output voltage V_(o).

FIG. 9 shows yet another example implementation of an electric powersystem 140 similar to the electric power systems 100 and 120 shown inFIGS. 7 and 8. In the implementation shown in FIG. 9, the electric powersystem 140 comprises a plurality of cell substrings 142 coupled to abalancing circuit 144. In this implementation, the balancing circuit 144comprises a plurality of substring DC-DC converters 146. Each substringDC-DC converter 146 has a primary port 148 and a secondary port 150. Theprimary port 148 is connected in parallel with a cell substring 142 soit can add or subtract the current in order to balance the cellsubstrings 142. The secondary ports 150 of the substring DC-DCconverters 146 are connected in parallel and are further coupled acrossthe power system output. Each substring DC-DC converter 146 furtherdetermines or receives a reference voltage proportional to the secondaryisolated port voltage.

FIGS. 10A through 10E show several embodiments of example cellsubstrings that may be used with the balancing circuits describedherein. FIG. 10A, for example, shows a photovoltaic cell substring 160comprising one or more series-connected photovoltaic (PV) cells withouta diode coupled in parallel to the cells, while FIG. 10B shows a secondphotovoltaic cell substring 162 in which a diode is coupled in parallelto the one or more of the series-connected cells of the substring 162.FIG. 10C shows a battery cell substring 164 comprising one or moreseries-connected electrochemical (battery) cells. FIG. 10D shows acapacitor cell substring 166 comprising one or more series-connectedcapacitors. FIG. 10E shows an electronic cell substring 168 comprisingone or more electrical or electronic components or modules. Although notshown in FIG. 10, a thermoelectric couple substring 170 may comprise oneor more series-connected thermoelectric couple cells.

FIG. 11 shows an example implementation of a battery system 180comprising a plurality of battery cells 182 connected in series and abalancing circuit 184. The balancing circuit 184 comprises a pluralityof isolated DC-DC converters 186. Each of the DC-DC converters 186 has aprimary port 188 connected across a battery cell 182, and a secondaryport 190 isolated from the primary port 188. The secondary ports 190 ofthe DC-DC converters 186 are connected in parallel to a secondary portV_(S) of the balancing circuit 184. The secondary port V_(S) of thebalancing circuit 184 is isolated. Each substring DC-DC converter 146further determines or receives a reference voltage proportional to thesecondary isolated port voltage, or a reference voltage proportional tothe battery system output voltage V_(o).

Control Techniques

In various implementations, a substring DC-DC converter in the balancingcircuits described herein has a controller 200 capable of adjusting aconverter primary port current in order to balance the cells. Thebalancing is accomplished by comparing the primary port voltage V_(p) tothe reference voltage V_(r) at a comparator 202, for example as shown inFIG. 12. In one particular implementation, an error V_(e) between theprimary port voltage and the reference voltage is processed by acompensator G_(c) to produce a control signal V_(c) at the input of amodulator 204. In response to the control signal V_(c), the modulator204 generates control signals for switches in the substring DC-DCconverter so that the primary port current I_(p) is proportional to thecontrol signal V_(c).

The reference voltage V_(r) can be proportional to the secondary portvoltage V_(s). This option can be applied in embodiments such as thoseshown in FIG. 4B, FIG. 7, FIG. 8, FIG. 9, or FIG. 11. Another option isto have the reference voltage V_(r) proportional to the system outputvoltage, as shown, for example, in FIGS. 17A and 17B. The controltechniques described here apply to either one or a combination of theseoptions available to generate the reference voltage V_(r). FIGS. 17A and17B show two implementations of balancing circuits 250, 260 comprisingsubstring DC-DC converters connected across cell substrings. FIG. 17A,for example, shows a case where a secondary port of the balancingcircuit 250 is isolated, while FIG. 17B shows a case where a secondaryport of the balancing circuit 260 is connected across the output of thestring of series-connected cell substrings. FIGS. 17A and 17B showexample implementations of an electrical system comprising a pluralityof series connected cells 252, 262 with a balancing circuit 254, 264. Inthe balancing circuits 254, 264, reference voltages are obtained by avoltage divider circuit 256, 266 with an isolated secondary port (FIG.17A) and with the secondary port connected across a string of seriesconnected cell substrings (FIG. 17B).

Consider the system with the balancing circuit shown in FIG. 7. ByKirchhoff's current law,

I _(o) =I ₁ −I _(p1) =I ₂ −I _(p2) =I ₃ −I _(p3)   (1)

By Kirchhoff's voltage low,

V _(o) =V _(p,1) +V _(p,2) +V _(p,3)   (2)

Consider further the case when the reference voltages are all equal andproportional to the system output voltage,

$\begin{matrix}{V_{r\; 1} = {V_{r\; 2} = {V_{r\; 3} = {V_{r} = {\frac{1}{3}V_{o}}}}}} & (3)\end{matrix}$

In one implementation, the compensator DC gain G_(c)(0)=G_(o) is afinite positive value, and

C _(c,i) =G _(o) V _(e,i) =G _(o)(V _(p,i) −V _(r))   (4)

The modulator controls the DC-DC converter so that the primary portcurrent is proportional to the control signal V_(c),

I _(p,i) =G _(m) V _(c,i) =G _(m) G _(o)(V _(p,i) −V _(r))=K _(o)(V_(p,i) −V _(r))   (5)

where K_(o)=G_(m)G_(o) is a finite, positive value. Solving Equation (5)for V_(p,i),

$\begin{matrix}{V_{p,i} = {V_{r} + {\frac{1}{K_{o}}I_{p,i}}}} & (6)\end{matrix}$

Inserting V_(p,i) for i=1, 2, 3 from Equation (6) into Equation (2),

$\begin{matrix}{V_{o} = {{V_{r} + {\frac{1}{K_{o}}I_{p,1}} + V_{r} + {\frac{1}{K_{o}}I_{p,3}} + V_{r} + {\frac{1}{K_{o}}I_{p,3}}} = {{3\; V_{r}} + {\frac{1}{K_{o}}\left( {I_{p,1} + I_{p,2} + I_{p,3}} \right)}}}} & (7)\end{matrix}$

which, taking into account Equation (3), implies that the balancingDC-DC controller results in

I _(p,1) +I _(p,2) +I _(p,3)=0   (8)

From Equation (1), it follows that the system output current is equal tothe average of the substring currents,

$\begin{matrix}{I_{o} = {{\frac{1}{3}\left( {I_{1} + I_{2} + I_{3}} \right)} = 0}} & (9)\end{matrix}$

The DC-DC converter primary port currents are:

$\begin{matrix}{I_{p\; 1} = {{I_{1} - I_{o}} = {{\frac{2}{3}I_{1}} - {\frac{1}{3}\left( {I_{2} + I_{3}} \right)}}}} & (10) \\{I_{p\; 2} = {{I_{2} - I_{o}} = {{\frac{2}{3}I_{2}} - {\frac{1}{3}\left( {I_{1} + I_{3}} \right)}}}} & (11) \\{I_{p\; 3} = {{I_{3} - I_{o}} = {{\frac{2}{3}I_{3}} - {\frac{1}{3}\left( {I_{1} + I_{2}} \right)}}}} & (12)\end{matrix}$

The corresponding primary port voltages can then be found from Equation(6). It can be observed that in this embodiment the controller resultsin primary-port voltages close to but not necessarily equal to thereference voltage. Gain K_(o) can be selected to adjust voltageregulation performance in the presence of mismatches. In the case whenall susbstrings are well matched, i.e. when I₁=I₂=I₃, Equations(10)-(12) show that the primary-port currents are all equal to zero. Inother words, in a well matched system, the DC-DC converters need notprocess any power.

Based on the control approach described above, each DC-DC converter canbe controlled autonomously, without the need for a central systemcontroller or any communication of control or sensing signals among theDC-DC converters. As a result, the control is simple and scalable to anynumber of DC-DC converters in the balancing circuit.

Many variations of the controller embodiments are possible. FIGS. 13Athrough 13C show several examples of controller compensator steady-state(DC) characteristics. FIG. 13A shows a gain G_(o). FIG. 13B shows a gainG_(o) with saturation limits, and FIG. 13C shows a gain G_(o) with deadzone and saturation limits. The frequency response G_(c)(s) can bedesigned to ensure stable and fast response of the balancing circuit.Furthermore, the controller modulator can have many differentembodiments, for example based on a pulse-width modulator, an on/offhysteretic modulator, or a current-mode modulator.

FIG. 14 shows another example implementation of a controller 210 for asubstring DC-DC converter in one or more of the balancing circuitsdescribed herein. In this implementation, a secondary port voltage V_(s)is further compared at a comparator 212 to a reference V_(rs), and thesecondary port voltage error V_(es) is used to modify a modulatorcontrol input V_(cp). The secondary-port voltage feedback loop isdesigned to regulate the secondary voltage to the secondary referenceV_(rs) so that in steady-state operation V_(s)=V_(rs), and the primaryvoltage control operates as previously described.

FIG. 18 shows an example implementation of a block diagram 270 of asubstring DC-DC converter controller based on an example controltechnique. In this implementation, a voltage proportional to a substringconverter primary port voltage V_(p) is compared at a comparator 272 toa reference V_(r). The reference V_(r) is proportional to a substringsecondary port voltage V_(s). An error signal, i.e. the differencebetween V_(p) and V_(r) is processed by a compensator G_(c). The outputof the compensator is the input to a modulator 274 that generatescontrol signals for the substring DC-DC converter, so that V_(p) isessentially regulated at a value set by V_(r). The compensator shown inFIG. 18 can be implemented using any of well-known control techniques.In the system of FIG. 7, for example, this control technique results inbalancing of series connected cell substrings, while simultaneouslyregulating the secondary port voltage V_(s).

When the substring DC-DC converter is a resonant converter where theprimary port current depends on a difference between the primary portand secondary port voltages, a simple open-loop switch control issufficient for balancing.

In various example implementations, a balancing circuit is provided fora series-connected cells or cell strings. In some of theseimplementations, the balancing circuits provide cell balancing andoptimization of system performance in terms of efficiency, power output,energy capture, energy storage capacity or lifetime under all or manyoperating conditions using DC-DC converter processing only a mismatchportion of system power. Where the DC-DC converters are processing onlya mismatch portion of the system power, the DC-DC converters in thebalancing circuit are rated at a portion of the system power, reducingthe overall system cost. Further, the balancing circuit can introduce noinsertion or other losses when the cells or strings of cells in thesystem are well matched. The control of DC-DC converters can beperformed locally, without the need for a central controller orcommunication of control and sensing signals. In addition, the balancingcircuit is scalable to systems with arbitrarily large number of cells inseries.

Filtering Series-Connected Cells

In a grid-tied PV system (e.g., FIGS. 2A-2C) or a photovoltaic systemwith an AC output, the mismatch between the DC output ofseries-connected cells, substrings or modules and the AC output iscommonly filtered using capacitors or other types of energy storagedevices. The required filtering components, typically based oncapacitive energy storage, are responsible for increased system cost,reduced system reliability or reduced efficiency of DC-AC inverters. Anactive filtering approach can be applied to reduce required energystorage and power processing related to filtering. The approach could beapplied to PV systems, but would require additional active components,and would result in reduced system efficiency.

In various implementations described herein, for AC-output systems(e.g., photovoltaic systems), a cost-effective, reliable filtering isalso provided in a simple and scalable cell balancing approach withbuilt-in filtering.

FIGS. 15A and 15B show an example implementation of a photovoltaicmodule 220 with a balancing and filtering circuit 222. The photovoltaicmodule 220 with balancing/filtering circuit 222 is similar to thebalancing circuits shown and described above (see, e.g., FIGS. 4A and4B), with an additional filter capacitor C_(s) disposed across theisolated secondary port.

In this implementation, the balancing/filtering circuit 222 is shown inphotovoltaic module having seventy two photovoltaic cells 224 arrangedin three substrings 226, 228, 230. Each substring includes twenty fourphotovoltaic cells 224 connected in series. The balancing/filteringcircuit 222 comprises a plurality of substring DC-DC converters 232. Asubstring DC-DC converter 232 has a primary port (voltage V_(p)) and anisolated secondary port (voltage V_(s)). The secondary port and theprimary port of the substring DC-DC converters 232 are isolated. Theprimary port of a substring DC-DC converter 232 is connected in parallelwith a substring 226, 228 or 230 of cells 224 in the photovoltaic module220. The secondary ports of all substring DC-DC converters 232 areconnected in parallel. Additionally, each substring DC-DC converter 232uses a reference voltage proportional to the secondary isolated portvoltage. The balancing circuit operates by diverting primary-portcurrent (I_(p)>0) from, or by injecting primary-port current (I_(p)<0)to the corresponding cell substring as described above. Furthermore, thefiltering capacitor C_(s) and the operating voltage V_(s) can beselected to provide filtering in AC-output PV systems using the moduleshown in FIGS. 15A and 15B.

FIG. 16A shows a photovoltaic system 240 where a module with built-inbalancing and filtering circuit 242, such as shown in FIG. 15B, iscoupled to an AC output 244 using a DC-AC inverter 246. The inverter 246shown could be, for example, a string inverter or a micro-inverter. Acontrol for the substring DC-DC converters 248 is the same as describedabove with reference to FIGS. 12 through 14, but with the referencevoltages V_(r) further filtered to substantially remove any componentsat the AC line frequency or harmonics of the AC line frequency. WithV_(r) reference voltages being essentially DC, the control approachdescribed in above achieves balancing and filtering simultaneously ornear simultaneously. As a result, V_(o)(t) is substantially DC voltagewith a small AC ripple, while I_(o)(t) can include substantial AC linefrequency components. For example, if output AC voltage v_(ac)(t) andoutput AC current i_(ac)(t) are substantially sinusoidal at AC linefrequency, I_(o)(t) is a rectified sinewave waveshape. The AC componentof I_(o)(t) is diverted through substring DC-DC converters 248, andfiltered by the energy-storage filtering capacitor C_(s) connectedacross the secondary port.

FIG. 16B shows example AC output waveforms of the balancing/filteringcircuit 242 shown in FIG. 16A. The AC output waveforms include an ACoutput voltage v_(ac)(t), an AC output current i_(ac)(t) and an ACoutput power p_(ac)(t). Energy E shows the amount of energy that may bedeposited on or restored from the energy-storage filtering capacitorC_(s) connected across the secondary port.

In a case when energy storage is integrated within the balancingcircuit, the reference V_(r) can be obtained by low-pass filtering thesecondary port voltage V_(s).

The same balancing/filtering circuit can also be applied to otherAC-output or AC-input power systems based on series connected cells orsubstrings, such as systems based on capacitors or super-capacitors,solid-state lighting (LED) systems, thermoelectric couples or othersystems with electrical or electronic components or modules connected inseries.

In various example implementations, a balancing and filtering circuit isprovided for a series-connected cells or cell strings. In some of theseimplementations, the balancing and filtering circuits provide effectivecell balancing and optimization of system performance in terms ofefficiency, power output, energy capture, energy storage capacity orlifetime accomplished under all or many operating conditions using DC-DCconverters processing only a mismatch portion of system power. Further,the balancing and filtering circuit can introduce no insertion or otherlosses when the cells or strings of cells in the system are wellmatched. In photovoltaic systems with an AC output, the filtering can beaccomplished actively, thus reducing the cost the requiredenergy-storage, filtering capacitors, while re-using the balancing DC-DCconverters. The filtering and improved reliability are accomplished atlow cost and at high efficiency. The control of the substring DC-DCconverters can be performed locally, without the need for a centralcontroller or communication of control and sensing signals. Thebalancing/filtering circuit is scalable to systems with arbitrarilylarge number of cells in series. Photovoltaic modules with a built-inbalancing/filtering circuit can also be used in all or many types ofphotovoltaic systems with an AC output.

Substring DC-DC Converters or Submodule Integrated DC-DC Converters(SubMICs)

Mismatched photovoltaic modules or systems exhibit nonconvex outputpower versus output voltage characteristics with multiple maxima thathinder operation of maximum power point (MPP) tracking algorithms andresult in the need to operate photovoltaic system power electronics overa wider range of MPP voltages.

Many photovoltaic architectures based on distributed power electronicscapable of module-level MPP tracking (MPPT) have been investigated,including DC-AC microinverters or DC-DC module-integrated converters(MICs). In these approaches, the impact of mismatches is reduced byperforming module-level MPPT, at the expense of insertion losses andincreased cost associated with the distributed power optimizers that arerequired to process full photovoltaic power even in the case when nomismatches are present.

FIG. 19 shows an example implementation diagram in which a centralcontroller and only one module-level current sensor, which could be thesame current sensor used for MPP tracking by downstream powerelectronics (e.g., a microinverter supplied by the module), are used. Aflowchart of an example control algorithm is shown in FIG. 21. Adisadvantage of the approach shown in FIG. 19 is that the centralcontroller must sense multiple voltages and issue multiple referencesignals to the subMlCs.

An alternative, distributed subMIC control approach that does notrequire a central controller is shown in FIG. 21. In this exampleimplementation, each subMIC can be controlled independently from theothers. In the discussion that follows, it is assumed that thesubMIC-enhanced PV module is attached to a converter (e.g., amicroinverter) that performs traditional MPP tracking using one of manyavailable methods. The module output voltage is set to the MPP valuev_(mod)=V_(d). Assuming that substrings have an identical number ofcells, power balance can be achieved by balancing substring voltages.Although the substring MPP voltage may change with operating conditions(such as irradiance and temperature), it is assumed in this example thatsuch changes can be considered relatively small. FIG. 20 shows asubstring and its corresponding subMIC that regulates the substringvoltage to a reference proportional to the secondary port voltagev_(mod).

A comparison between various SubMIC control schemes is disclosed inOlalla, C., Clement, D., Rodriguez, M. and Maksimovic, D., Architecturesand Control of Submodule Integrated DC-DC Converters for PhotovoltaicApplications, IEEE Trans. On Power Electronics, Vol. 28, No. 6, June2013 pp. 2980-2997, which is incorporated herein by reference as if itwere set forth in its entirety, and is also included in United Statesprovisional patent application number 61785196, filed on March 14, 2013,which is also incorporated by reference in its entirety. As discussedtherein, in practice, photovoltaic modules have a relatively smallnumber of substrings and worst case solutions for the proposed controlapproach are much closer to the optimal. For a considered typical modulewith three substrings, in the worst case, the optimal solutioncorresponds to P_(opt)=V_(ref) I_(g), while the proposed distributedcontrol approach yields P_(subopt)=4/3 V_(ref) I_(g). In other words,the worst case power processed by the subMlCs using the simple,distributed control approach is 33% higher than the optimum.

In addition to the very simple distributed implementation, the proposedsuboptimal control approach has another important advantage in that itallows subMlCs with lower power rating, since power is distributedfollowing equations (18) and (19), so that subMIC power rating can bereduced to (ns −1)/ns of subMIC power rating with the optimal approach.In the considered typical PV module example with three substrings, thesubMIC power rating is equal to 67% of the subMIC power rating requiredto implement the optimal solution.

The steady-state solution of the suboptimal control approach yields animportant conclusion about its behavior. Since substring currents arebalanced to an average value, the sum of primary/secondary subMICcurrents is zero. This means that all power transferred to the secondaryport of subMlCs is absorbed by the remaining subMlCs, and therefore, thesecondary port average power is zero. This implies that the secondaryport of the subMlCs can be disconnected from the module output, leadingto an isolated-port architecture.

It should also be noted that the subMIC secondary port of a module canbe connected in parallel with the subMIC secondary port of anothermodule. In turn, such subMIC-enhanced modules with shared secondaryports can be connected in series to form larger PV arrays in much thesame way traditional PV systems are realized, but with the advantage ofbuilt-in balancing (see FIG. 22). The extension of the isolated-portarchitecture to arbitrarily long chains of series-connected substringsor modules and to arbitrarily high dc voltages does not impact subMICpower or voltage rating, with an exception of the transformer dcisolation voltage rating. It is also worth noting that active filteringcan be implemented with an energy storage capacitor on the subMICisolated port, as shown in FIG. 16A, with potentials to reduce the costand improve efficiency of downstream power electronics connected to thesubMIC-enhanced module or a string of subMIC-enhanced modules.

FIG. 23 shows an example implementation in which each subMIC isimplemented as a bidirectional flyback converter. This topology providesisolation and bidirectional power transfer capabilities. Operation inDCM eliminates diode reverse recovery losses, thus allowing highefficiency. Furthermore, when the converter is operated in DCM, itexhibits simpler dynamic behavior, allowing a simpler controller design,as well as faster changes in the direction of power transfer.

In order to transfer power from primary to secondary side, Q_(pri) iscontrolled using a conventional, constant-frequency pulse-widthmodulation with a duty cycle D=(T_(on)/T_(s)), with T_(on) being aswitch on time and T_(s) being the switching period. The secondary-sideswitch Q_(sec) remains OFF at all times, and its body diode acts as aflyback diode. To reverse the power transfer direction, the converter isoperated in a completely symmetrical manner: Qpri remains OFF during thecomplete switching period, its body diode acts as the flyback diode, andQsec is now controlled in the manner described previously. The flybackimplementation of each subMIC includes capacitances both in the primaryC_(pri) and secondary side C_(sec). Given that all subMlCs are ideallyidentical, the total secondary capacitance in the proposed architectureis C_(seq)=C_(sec)·n_(s). The primary-side magnetizing inductanceL_(pri) is chosen to maintain DCM under all operating conditions.

FIGS. 24A and 24B show example implementations of a photovoltaic systems280, 290. In FIG. 24A, for example, the photovoltaic system 280comprises a SubMIC-enhanced module 282 and a microinverter 284. Themicroinverter 284 can be a single-phase or three-phase microinverter. InFIG. 24B, however, the photovoltaic system 290 comprises aSubMIC-enhanced module 292 and a DC optimizer 294. The DC optimizer 294output can be connected in series or parallel.

FIG. 26 shows a photovoltaic system 300 comprising a string ofSubMIC-enhanced modules 302 and one or more string inverters or acentral inverter 304. The inverter(s) can be single-phase orthree-phase.

FIG. 27 shows a photovoltaic system 310 comprising a string ofSubMIC-enhanced modules and one or more string inverters or a centralinverter. The inverters can be single-phase or three-phase. In thisimplementation, an isolated secondary port is shared among the modules.The isolated secondary port can also be used to sense and reportmeasurements or operational status of modules.

Although many implementations have been described above with a certaindegree of particularity, those skilled in the art could make numerousalterations to the disclosed implementations without departing from thespirit or scope of this invention. For example, although many exampleimplementations are provided in conjunction with photovoltaic cells andmodules, the various implementations may be used in conjunction with anyother type of electrochemical, electrical or electronic cell, such as,but not limited to, series-connected cells or substrings includingsystems based on battery cells, capacitors or super-capacitors,solid-state lighting (LED) systems, thermoelectric couples or othersystems with electrical or electronic components or modules connected inseries. All directional references (e.g., upper, lower, upward,downward, left, right, leftward, rightward, top, bottom, above, below,vertical, horizontal, clockwise, and counterclockwise) are only used foridentification purposes to aid the reader's understanding of the presentinvention, and do not create limitations, particularly as to theposition, orientation, or use of the invention. Joinder references(e.g., attached, coupled, connected, and the like) are to be construedbroadly and may include intermediate members between a connection ofelements and relative movement between elements. As such, joinderreferences do not necessarily infer that two elements are directlyconnected and in fixed relation to each other. It is intended that allmatter contained in the above description or shown in the accompanyingdrawings shall be interpreted as illustrative only and not limiting.Changes in detail or structure may be made without departing from thespirit of the invention as defined in the appended claims.

What is claimed is:
 1. A balancing circuit comprising: a plurality ofprimary ports; an isolated secondary port; and one or more DC-DCconverters connected between the primary ports and the isolatedsecondary port, each DC-DC converter comprising at least one powerswitch, the DC-DC converters configured to adjust a primary port currentreceived at one or more of the plurality of primary ports based upon adifference between a voltage at the one of the primary ports and areference voltage.
 2. The balancing circuit of claim 1 wherein thereference voltage is derived from at least one of: a secondary portvoltage, and a system output voltage of a series connected cell powersystem.
 3. The balancing circuit of claim 1 wherein the balancingcircuit comprises at least one controller configured to adjust theprimary port current by adjusting a control input for at least one powerswitch in the one or more DC-DC converters.
 4. The balancing circuit ofclaim 3 wherein the control input is at least one of (i) a duty cycleand (ii) a switching frequency.
 5. The balancing circuit of claim 3wherein the at least one controller is configured to adjust the controlinput for at least one power switch based on at least one of (i) thedifference between the voltage at the first primary port and thereference voltage, and (ii) the input derived from the system outputvoltage.
 6. The balancing circuit of claim 3 wherein the at least onecontroller is configured to adjust the control input for at least onepower switch in proportion to the difference between the voltage at theone of the primary ports and the voltage at the isolated secondary port.7. The balancing circuit of claim 1 wherein the primary port current ofthe DC-DC converter is proportional to the difference between a voltageat the one of the primary ports and a voltage at the isolated secondaryport.
 8. The balancing circuit of claim 1 wherein the isolated portcomprises a monitoring signal.
 9. The balancing circuit of claim 1wherein the monitoring signal comprises at least one of a powerindication, a temperature indication, a functionality indication, and afailure indication.
 10. The balancing circuit of claim 1 wherein afiltering capacitor is connected across the isolated secondary port. 11.An electric power system comprising: a plurality of cell substrings anda balancing circuit, the cell substrings comprising one or more cellsconnected in series, and the balancing circuit comprising a plurality ofisolated DC-DC converters, the isolated DC-DC converters comprising: atleast one power switch, a primary port connected in parallel with aphotovoltaic cell substring, and an isolated secondary port connected inparallel with isolated secondary ports of other isolated DC-DCconverters.
 12. The electric power system of claim 11 wherein theplurality of cell substrings comprises a plurality of photovoltaic cellsubstrings comprising one or more photovoltaic cells connected inseries.
 13. The electric power system of claim 12 wherein the balancingcircuit is configured to receive a reference input derived from thesystem output voltage.
 14. The electric power system of claim 13 whereinthe balancing circuit comprises a controller configured to adjust aprimary port current in response to a difference between a primary portvoltage and the reference voltage.
 15. The electric power system ofclaim 11 wherein the balancing circuit is configured to adjust a primaryport current received at one or more of the plurality of primary portsbased at least in part on a reference input derived from a voltage atthe isolated secondary port.
 16. The electric power system of claim 16where the one or more cells comprise at least one of the following: aphotovoltaic cell, an energy storage cell, a battery cell, a capacitor,a thermoelectric couple, an electronic device, or an electronic module.17. The electric power system of claim 10 wherein the electric powersystem is configured to be coupled to an AC electric grid via at leastone of a microinverter, a string inverter and a central inverter. 18.The electric power system of claim 10 wherein a filtering capacitor isconnected across the isolated secondary port.
 19. The electric powersystem of claim 10 wherein the balancing circuit is configured to thereference input is derived from the secondary port voltage
 20. A methodof balancing a plurality of electric cell substrings, the methodcomprising: coupling a primary port of a first DC-DC converter inparallel with a first cell substring; coupling a primary port of asecond DC-DC converter in parallel with a second cell substring;coupling an isolated secondary port of the first DC-DC converter inparallel with an isolated secondary port of the second DC-DC converter;adjusting a primary port current received at at least one of the primaryports based upon a difference between a voltage at the one of theprimary ports and a reference voltage.
 21. The method of claim 20wherein the plurality of electrical cell substrings comprise at leastone cell selected from the group comprising: a photovoltaic cell, anenergy storage cell, a battery cell, a capacitor, a thermoelectriccouple, an electronic device, or an electronic module.
 22. The method ofclaim 20 wherein the primary port current of the first DC-DC converteris proportional to a difference between a voltage at the one of theprimary ports and a voltage at the isolated secondary port.
 23. Themethod of claim 20 wherein each of the DC-DC converters comprises acontroller configured controller configured to adjust the primary portcurrent by adjusting a control input for at least one power switch inone or more of the first and second DC-DC converters.